A.—­In the feathering wheel, where every part of any one immerged float moves forward with the same horizontal velocity, the pressure or resistance may be supposed to be concentrated in the centre of the float; whereas, in the common radial wheel this cannot be the case, for as the outer edge of the float moves more rapidly than the edge nearest the centre of the wheel, the outer part of the float is the most effectual in propulsion.  The point at which the outer and inner portions of the float just balance one another in propelling effect, is called the centre of pressure; and if all the resistances were concentrated in this point, they would have the same effect as before in resisting the rotation of the wheel.  The resistance upon any one moving float board totally immersed in the water will, when the vessel is at rest, obviously vary as the square of its distance from the centre of motion—­the resistance of a fluid varying with the square of the velocity; but, except when the wheel is sunk to the axle or altogether immersed in the water, it is impossible, under ordinary circumstances, for one float to be totally immersed without others being immersed partially, whereby the arc described by the extremity of the paddle arm will become greater than the arc described by the inner edge of the float; and consequently the resistance upon any part of the float will increase in a higher ratio than the square of its distance from the centre of motion—­the position of the centre of pressure being at the same time correspondingly affected.  In the feathering wheel the position of the centre of pressure of the entering and emerging floats is continually changing from the lower edge of the float—­where it is when the float is entering or leaving the water—­to the centre of the float, which is its position when the float is wholly immerged; but in the radial wheel the centre of pressure can never rise so high as the centre of the float.

553. Q.—­All this relates to the action of the paddle when the vessel is at rest:  will you explain its action when the vessel is in motion?

A.—­When the wheel of a coach rolls along the ground, any point of its periphery describes in the air a curve which is termed a cycloid; any point within the periphery traces a prolate or protracted cycloid, and any point exterior to the periphery traces a curtate or contracted cycloid—­the prolate cycloid partaking more of the nature of a straight line, and the curtate cycloid more of the nature of a circle.  The action of a paddle wheel in the water resembles in this respect that of the wheel of a carriage running along the ground:  that point in the radius of the paddle of which the rotative speed is just equal to the velocity of the vessel will describe a cycloid; points nearer the centre, prolate cycloids, and points further from the centre, curtate cycloids.  The circle described by the point whose velocity equals the velocity of the ship,